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A glass tube filled with colored water, sealed at both the ends is bent into an arc. There is small air bubble inside. The tube is held with its plane vertical. When the tube moves with constant acceleration either to left or right the bubble shifts and settles at some position either to the left or right of the highest point. For the situation shown , what can you conclude about acceleration vector of the tube?

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.it points towards the left.

It points towards the right

Its magnitude is $g \tan θ$

Its magnitude is $g c o t θ$

answer is A, C.

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Detailed Solution

Free body diagram is:

Here $ρ_{w} V g = V e r t i c a l c o m p o n e n t o f r e s u l \tan t f o r c e e x e r t e d b y w a t e r o n t h e b u b b l e .$

and $ρ_{w} V a = H o r i z o n t a l c o m p o n e n t o f r e s u l \tan t f o r c e e x e r t e d b y w a t e r o n t h e b u b b l e .$

Resultant of $ρ_{w} V_{g}$ & $ρ_{w} V_{a}$ should be exactly opposite to $N$ i.e., $\tan θ = \frac{a}{g} \Rightarrow a = g \tan θ$

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